Fuzzy Set Theory and Nonlinear Models

Abstract

The fuzzy set operators for intersection and union immediately suggest a class of nonlinear models for predictive or causal analysis because of their connection with “and” and “or”. This class includes any predictive model with at least two independent variables connected by an appropriate version of “and” or “or”. Before fuzzy set theory, these models were definable only for dichotomous variables and did not enjoy much popularity in the behavioral sciences. However, many examples of theories using “and” and “or” connectives may be found in several fields, and some methodologists have acknowledged their importance as a kind of interaction model (e.g., the so-called “Conduciveness model” in Southwood’s 1978 typology of interaction models). The attraction of “and” and “or” models stems mainly from their intuitive plausibility under some conditions and their easy interpretation in natural language terms. Indeed, the commonsense causal statement that “Y is present only if both A and B are present” often is used as an introductory teaching example of interaction in methods courses.